The present invention relates to a method and a device for compensating for position-dependent length changes caused by the effect of weight in a plurality of closed kinematic chains for connecting a stationary first element to a movable second element, on which a weight acts, respective actuators being assigned to the kinematic chains, via which a relative movement between the first and the second element is predefined in a freely definable sequence of control instructions, by the respective positions of the respective actuators required for desired positions of the movable element being determined via a back transformation Λ−1, in particular for parallel kinematic systems for use in numerically controlled machine tools and robots.
Such aforementioned parallel kinematic systems are being employed to an increasing extent in machine tools and industrial robots. In this case, a parallel kinematic system constitutes a three-dimensional coupling mechanism which comprises at least one closed kinematic chain. The kinematic chain, for its part, is used to connect a fixed frame platform to a movable working platform. Kinematic chains in this case comprise either links and connecting elements of constant or variable length. In the illustrations according to FIGS. 2 and 3, two different embodiments of parallel kinematic systems according to the prior art are shown, which are used in machine tools and robots. Here, FIG. 2 shows a parallel kinematic system with invariable-length connecting elements, while FIG. 3 shows one such with variable-length connecting elements, which are in each case driven by associated actuators. Shown in each case is a frame platform P1, which is connected to a movable working platform P2 via links G1 . . . Gn and connecting elements V1 . . . Vn. In each case a weight Fg acts on the working platform P2, which represents an inertial mass.
As compared with conventional machine tools and serial robots, parallel kinematics are distinguished by their high dynamics and stiffness. The advantage of parallel kinematic systems consists inter alia in the fact that forces act predominantly axially on the movable connecting elements. Nevertheless, even in parallel kinematic systems, the problem arises that the connecting elements and links change their length as a result of the effect of weight or processing forces, which leads to positioning errors of the working point (working platform P2).
These length changes of the kinematic chains lead to position errors of the working point and impair the production quality. In the case of conventional machine tools, this leads to a positioning accuracy of about 10 μm. The aforementioned length changes are of approximately the same order of magnitude.
In the case of conventional machines with mutually perpendicular actuators, linear axes as they are known, the length changes caused by a constant weight are taken into account axis by axis in the form of a measured correction table and are compensated for in this way. Hitherto, however, there has been no remedy for the problem outlined in parallel kinematic systems and in general in closed kinematic chains for connecting a stationary first element to a movable second element, on which a weight acts.
It is therefore an object of the present invention to permit compensation of the position-dependent length change caused by the effect of weight in kinematic chains.